Find small tasks that you can accomplish. Like any large undertaking, learning a new language is a process. Approach it as such, with both short term tasks to keep your confidence up and longer term goals that will be highly rewarding.

If you are already proficient in another language, look for programs that are well suited for porting to perl.

If you are a beginning programmer, search out simple beginner's tutorials and work through them until you fully understand them.

Play with the language. Like web programming, check out CGI. Scraping pages more to your liking? There's WWW::Mechanize. Have uses for automating ftp/ssh/etc? Check out Net::FTP and the like.

Speaking of modules, become familiar with cpan. Many wheels have already been invented there, which will save you the trouble.

And then just spend time here. Pay attention to those who have been around (such as Grandfather, who gave some excellent advice already). Most of what I've learned about perl I've learned by watching, listening, helping where I can, and looking for problems that I could use perl to solve.